Optical pattern projection

ABSTRACT

Optical apparatus includes first and second diffractive optical elements (DOEs) arranged in series to diffract an input beam of radiation. The first DOE is configured to apply to the input beam a pattern with a specified divergence angle, while the second DOE is configured to split the input beam into a matrix of output beams with a specified fan-out angle. The divergence and fan-out angles are chosen so as to project the radiation onto a region in space in multiple adjacent instances of the pattern.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No.12/840,312, filed Jul. 21, 2010, which claims the benefit of U.S.Provisional Patent Application 61/229,749, filed Jul. 30, 2009, and is acontinuation-in-part of U.S. patent application Ser. No. 12/330,766,filed Dec. 9, 2008, and published as US 2009/0185274, which claims thebenefit of U.S. Provisional Patent Application 61/022,482, filed Jan.21, 2008. The disclosures of all of these related applications areincorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates generally to optical systems and designs,and specifically to methods and system for optical pattern projection.

BACKGROUND OF THE INVENTION

Optical pattern projection is used in a variety of applications, such asoptical three-dimensional (3D) mapping, area illumination, and LCDbacklighting. In some applications, diffractive optical elements (DOEs)are used in creating a desired projection pattern.

Various methods are known in the art for designing DOEs. In some ofthese methods, the DOE is designed as a phase mask, which corresponds,in effect, to a Fourier transform of the far-field amplitude patternthat the DOE is to project. A method for computing such phase masks isdescribed, for example, by Gerchberg and Saxton in “A PracticalAlgorithm for the Determination of the Phase from Image and DiffractionPlane Pictures,” Optik 35 (1972), pages 237-246, which is incorporatedherein by reference. Fienup reviews computational approaches that may beused in designing phase-mask DOEs in “Phase Retrieval Algorithms: AComparison,” Applied Optics 21, 2758-2769 (1982), which is alsoincorporated herein by reference.

Sazbon et al. describe how the Gerchberg-Saxton algorithm may be used indesigning a DOE for use in range estimation, in “Qualitative Real-TimeRange Extraction for Preplanned Scene Partitioning Using Laser BeamCoding,” Pattern Recognition Letters 26 (2005), pages 1772-1781, whichis also incorporated herein by reference.

SUMMARY

Embodiments of the present invention that are described hereinbelowprovide improved methods and apparatus for projection of opticalpatterns using DOEs.

There is therefore provided, in accordance with an embodiment of thepresent invention, optical apparatus, including first and seconddiffractive optical elements (DOEs) arranged in series to diffract aninput beam of radiation. The first DOE is configured to apply to theinput beam a pattern with a specified divergence angle, while the secondDOE is configured to split the input beam into a matrix of output beamswith a specified fan-out angle. The divergence and fan-out angles arechosen so as to project the radiation onto a region in space in multipleadjacent instances of the pattern.

In some embodiments, the divergence and fan-out angles are chosen sothat the multiple adjacent instances of the pattern tile the region. Inone such embodiment, the divergence angle of each instance of thepattern is 2β_(Tile), and the fan-out angle between the adjacentinstances is β_(FO), and the divergence and fan-out angles are chosen sothat sin(β_(FO))=2 sin (β_(Tile)). Typically, the first and second DOEsare configured so that the multiple adjacent instances of the patterntile the region irrespective of a wavelength of the input beam.Additionally or alternatively, each of the multiple adjacent instancesincludes multiple diffraction orders, including respective extremeorders, and the extreme orders of neighboring instances are mutuallyadjacent in a spatial frequency space.

In a disclosed embodiment, the pattern includes an uncorrelated patternof spots.

The second DOE may be configured to distribute an energy of the inputbeam among the output beams in accordance with a predefined non-uniformdistribution.

Typically, a diffraction pattern of the apparatus includes a zero-ordercomponent, and the first and second DOEs are configured to diffract theinput beam so that the zero-order component contains no more than 1% ofan energy of the input beam.

In one embodiment, the matrix of the output beams includes at least a3×3 matrix.

There is also provided, in accordance with an embodiment of the presentinvention, mapping apparatus, including a projection subassembly, whichincludes a radiation source, which is configured to generate an inputbeam of radiation. First and second diffractive optical elements (DOEs)are arranged in series to diffract the input beam, wherein the first DOEis configured to apply to the input beam a pattern with a specifieddivergence angle, while the second DOE is configured to split the inputbeam into a matrix of output beams with a specified fan-out angle, so asto project the radiation onto a region in space. An image capturesubassembly is configured to capture an image of the pattern appearingon an object in the region. A processor is configured to process theimage so as to produce a three-dimensional (3D) map of the object.

There is additionally provided, in accordance with an embodiment of thepresent invention, a method for projection, including directing an inputbeam of radiation to pass in series through first and second diffractiveoptical elements (DOEs), wherein the first and second DOEs areconfigured as described above.

The present invention will be more fully understood from the followingdetailed description of the embodiments thereof, taken together with thedrawings in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic, pictorial illustration of a system for optical 3Dmapping, in accordance with an embodiment of the present invention;

FIG. 2 is a schematic side view of a projection assembly, in accordancewith an embodiment of the present invention; and

FIG. 3 is a schematic frontal view of a plane illuminated using theassembly of FIG. 2, in accordance with an embodiment of the presentinvention.

DETAILED DESCRIPTION OF EMBODIMENTS

The above-mentioned U.S. Patent Application Publication 2009/0185274describes an optical design in which a first DOE diffracts an input beamso as to generate a first diffraction pattern on a first region of asurface. A second DOE diffracts the zero-order beam of the firstdiffraction pattern so as to generate a second diffraction pattern on asecond region of the surface, such that the first and the second regionstogether at least partially cover the surface.

In an alternative embodiment, the first diffraction pattern comprises aplurality of substantially collimated beams. The second DOE serves as apattern generator, to diffract each of the beams to form a respectivediffraction pattern. Each diffraction pattern projects onto a respectiveregion of a surface so as to at least partially cover the surface, andthe regions may tile the surface. The terms “first” and “second” areused solely for convenience in referring to the DOEs, and in practicethe input beam may pass through the two DOEs in any order—“first” then“second,” or vice versa.

In the specification and in the claims of the present patentapplication, a “tiling” of a region (whether a planar region or a regionin space) with a pattern means that the region is covered by multipleadjacent instances (“tiles”) of the pattern, without substantialoverlaps or gaps between the instances. When the pattern is made up ofspots, as in the embodiments described below, “substantial” means thatthe gaps and overlap between adjacent tiles are no greater than a small,predetermined number times the average dimension of the spots in thepattern. The number depends on application requirements, and istypically between one and five. In embodiments of the present inventionthat are described hereinbelow, appropriate design and fabrication ofthe DOEs can yield tiling with gaps and/or overlap no greater than twicethe average spot dimension, or even no greater than the average spotdimension itself.

In some embodiments of the present invention, DOEs of the typesdescribed above are used to project a pattern onto an object forpurposes of 3D mapping. In the present patent application and in theclaims, the term “3D map” (or equivalently, “depth map”) refers to a setof 3D coordinates representing the surface of the object. The creationof such a map based on image data is referred to herein as “3D mapping”(or equivalently, “3D reconstruction”). Methods and systems for 3Dmapping based on projected patterns are described, for example, in PCTInternational Publications WO 2007/043036, WO 2007/105205, WO2008/120217, and WO 2010/004542, whose disclosures are incorporatedherein by reference. DOEs designed in accordance with embodiments of thepresent invention have advantages, in this context, of covering a largemapping region with a pattern of high quality and well-controlledintensity, so that depth values may be found reliably over the entireregion. This intensity control is important particularly in ensuringthat the intensity is within eye safety limits when the region to bemapped includes human beings. Embodiments of the present inventioninherently provide beneficial safety margins of this sort.

FIG. 1 is a schematic, pictorial illustration of a system 20 for optical3D mapping, in accordance with an embodiment of the present invention.System 20 comprises an imaging device 24, comprising a projectionsubassembly 30, which generates and projects a pattern onto a region. Inthe pictured example, this region contains a human user 22 of thesystem. Details of the design and operation of projection subassembly 30are shown in the figures that follow and are described hereinbelow withreference thereto.

An image capture subassembly 32 in device 24 captures an image of thepattern appearing on user 22. An image processor 26 processes image datagenerated by device 24 in order to reconstruct a 3D map of user 22.Image processor 26 computes the 3D coordinates of points on the surfaceof the user's body by triangulation, based on the transverse shifts ofthe spots in an image of the pattern that is projected onto the objectrelative to a reference pattern at a known distance from device 24.Methods for this sort of triangulation-based 3D mapping, as well asfurther details relevant to the construction and operation of device 24,are described in the above-mentioned PCT publications. Alternatively,the types of DOEs and design techniques that are described hereinbelowmay be used in other sorts of depth mapping systems, not necessarilytriangulation-based. More generally, such DOEs and techniques can beused in substantially any application requiring eye-safe projection ofDOE-based patterns.

Image processor 26 may comprise a general-purpose computer processor,which is programmed in software to carry out the functions describedhereinbelow. The software may be downloaded to processor 26 inelectronic form, over a network, for example, or it may alternatively beprovided on tangible storage media, such as optical, magnetic, orelectronic memory media. Alternatively or additionally, some or all ofthe functions of the image processor may be implemented in dedicatedhardware, such as a custom or semi-custom integrated circuit or aprogrammable digital signal processor (DSP). Although processor 26 isshown in FIG. 1, by way of example, as a separate unit from imagingdevice 24, some or all of the processing functions of processor 26 maybe performed by suitable dedicated circuitry within the housing ofimaging device 24 or otherwise associated with the imaging device.

The 3D map that is generated by processor 26 may be used for a widerange of different purposes. For example, the map may be used to providea gesture-based user interface, in which user movements detected bymeans of device 24 control an interactive computer application, such asa game, and interact with objects shown on a display 28. Alternatively,system 20 may be used to create 3D maps of objects of other types, forsubstantially any application in which 3D coordinate profiles areneeded.

In some embodiments, projection subassembly 30 projects an uncorrelatedpattern of spots onto a given field of view. In the context of thepresent patent application and in the claims, the term “uncorrelatedpattern” refers to a projected pattern of spots (which may be bright ordark), whose positions are uncorrelated in planes transverse to theprojection beam axis. The positions are uncorrelated in the sense thatthe auto-correlation of the pattern as a function of transverse shift isinsignificant for any shift larger than the spot size and no greaterthan the maximum shift that may occur over the range of depths mapped bythe system. Random and pseudo-random patterns are uncorrelated in thissense. Synthetic patterns, created by human or computer design, such asquasi-periodic patterns, may also be uncorrelated to the extentspecified by the above definition. Alternatively, the projectionassembly and the DOE arrangements that are described hereinbelow may beused to project patterns of other sorts, not necessarily uncorrelated.

FIG. 2 is a schematic side view of a projection assembly 40, inaccordance with an embodiment of the present invention. Assembly 40 maybe used, for example, as part of projection subassembly 30 in imagingdevice 24 (FIG. 1). Assembly 40 comprises a light source 42, such as alaser diode, which generates and projects an input beam 44 of radiation(possibly collimated) via optics 46 onto a surface 54. Optics 46generate a pattern on the surface, as described further hereinbelow.Although surface 54 is shown in the figures, for the sake of simplicity,as a planar surface, the pattern is projected by the optics through aregion in space, and will thus cover an irregular surface of an objectwithin the beam area.

Optics 46 in the embodiment of FIG. 2 comprise two elements 48, 50,which typically comprise DOEs. Each DOE comprises a active opticalsurface, which is etched, molded or deposited on a suitable substrate,using methods known in the art. The active surfaces may be on eitherside of elements 48 and 50. In one embodiment, both active surfaces facetoward light source 42 (on the left sides of the respective substratesin the pictured embodiment). Alternatively, the two active surfaces maybe formed on opposing sides of the same substrate, in which case asingle optical component comprises, in effect, two DOEs. Furtheralternatively or additionally, the left/right order of the elements maybe reversed, so that beam 44 strikes element 50 before element 48. Inthe context of the present patent application and in the claims, eitherorder of the elements—element 48 before element 50 or vice versa—isconsidered to be an arrangement of elements 48 and 50 “in series” todiffract the input beam.

Element 48 applies a certain pattern to input beam 44, such as anuncorrelated pattern for use in the 3D mapping application describedabove. In order to project the pattern onto surface 54 over a wideangular range, element 50 splits the beam into a fanned-out matrix ofoutput beams 52. In the pictured example, element 50 creates nine beams,in a 3×3 fan-out. Alternatively, element 50 may be designed to giveother fan-out patterns, such as 5×5, 7×7, or patterns with unequalnumbers of beams in the vertical and horizontal directions.

Together, elements 48 and 50 project a pattern over a field of view(FOV) with full angular extent α_(FOV) in the horizontal direction andβ_(FOV) in the vertical (which is shown in the side view of FIG. 2).Element 50 spreads output beams apart with fan-out angles α_(FO)(horizontal) and β_(FO) (vertical) between adjacent beam axes. Each beamcarries an instance of the pattern generated by element 48, with fulldivergence angles 2α_(Tile) (horizontal) and 2β_(Tile) (vertical). Inthe 3×3 fan-out example shown in the figures, with pattern instances inbeams 52 that are mutually adjacent:α_(FOV)=2 arcsin(sin(α_(FO))+sin(α_(Tile))) and  (1a)β_(FOV)=2 arcsin(sin(β_(FO))+sin(β_(Tile))).  (1b)

These relations may be modified in a straightforward manner for othertiling schemes. For example, for (2n+1)×(2n+1) tiling:α_(FOV)=2 arcsin(n*sin(α_(FO))+sin(α_(Tile))), and  (2a)β_(FOV)=2 arcsin(n*sin(β_(FO))+sin(β_(Tile))).  (2b)

FIG. 3 is a schematic frontal view of a pattern 60 that is projected onsurface 54 by assembly 40, in accordance with an embodiment of thepresent invention. Pattern 60 comprises multiple adjacent instances,represented by tiles 56, of the pattern generated by element 48. Eachtile 56 is formed by a respective beam 52 and comprises a predefineddistribution of light spots 58 on a dark background (with light and darkreversed in the figure for clarity of representation). The DOEs ofelements 48 and 50 are designed so that tiles 56 precisely tile plane54. In other words, the tiles meet along their edges without substantialgaps or overlap.

Element 48 is typically designed to give an approximately uniformdensity of spots in each tile 56. In order to avoid problems due tooverlap of the tile edges, the spot pattern may be tailored to removespots in certain positions immediately adjacent to the tile edge thatare likely to overlap spots near the edge of the neighboring tile.

Referring back to FIG. 2, the divergence angles 2α_(Tile) and 2β_(Tile)refer to the effective angular outer limits of the pattern cast by asingle output beam 52 onto the corresponding tile 56. There will alwaysbe some energy in the output beam that escapes the confines of the tile,but element 48 may be designed to limit this stray energy to aninsignificant level, i.e., a level that does not substantially affectthe performance of the application, such as 3D mapping, for which thepattern is projected. Typically, more than 80% of the energy in a givenoutput beam is contained within the specified divergence angles, butlarger or smaller limits may be applied depending on applicationrequirements and manufacturing and design constraints.

The phase mask of element 50 comprises a periodic pattern of repeatingcells. The dimensions of the cells in the pattern control the fan-outangle between tiles 56, which correspond to different diffraction ordersof the periodic pattern. In the example shown in FIGS. 2 and 3, for thecase of 3×3 tiling, the dominant spatial frequencies of the phase maskof element 50 are typically roughly twice those of element 48 along boththe X and Y axes in order to give the desired relation between thespecified fan-out and divergence angles.

In this manner, the tiling conditions may be translated into designconsiderations for the DOEs. For perfect, gapless tiling, with element48 having (2M+1)×(2M+1) diffraction orders (some of which are off, thuscreating the tile pattern), the grating period of the phase mask inelement 48 will be equal to (M+0.5) times the grating period of element50. For example, if the tile pattern is 21×21, and the grating period ofelement 50 is 5 μm, then the period of the unit cell in element 48 willbe 10.5*5 μm=52.5 μm. The grating periods of element 50 in the X and Yaxes, respectively, is determined from the total required field of view,using relations (1a), (3a) and (1b), (3b) below. The grating period ofelement 48 is then determined from the perfect tiling conditiondescribed here and specified by the formulas below.

The shape of the phase mask within each cell of element 50 controls thepower distribution among the different output beams (diffractionorders). Thus, element 50 may be designed to give either uniform lightintensity distribution among tiles 56 or a predefined non-uniformintensity distribution. For example, a larger relative share of theinput beam energy (typically on the order of 15-30%) may be directed tothe corner tiles in order to compensate for geometric factors andvignetting by the image capture subassembly that is used to captureimages of the projected pattern. Element 50 may thus be designed to givethe appropriate share of energy to each beam 52 in order to optimizesystem performance.

In the pictured embodiment, to provide perfect tiling within aprescribed field of view, the fan-out and divergence angles meet theconstraints defined above in equations (1a) and (1b):α_(FOV)=2 arcsin(sin(α_(FO))+sin(α_(Tile)))  (1a)β_(FOV)=2a sin(sin(β_(FO))+sin(β_(Tile)))  (1b)and also satisfy the relations:sin(α_(FO))=2 sin(α_(Tile))  (3a)sin(β_(FO))=2 sin(β_(Tile)).  (3b)For the general case of (2n+1)×(2n+1) tiling, equations (1a) and (1b)are replaced by equations (2a) and (2b), as described above, whileequations (3a) and (3b) are unchanged. DOEs satisfying these relationsachieve tiling without gaps, wherein the tile borders match exactly,meaning that the extreme orders of the adjacent tiles coincide inspatial frequency space.

For some applications, a small gap is beneficial, and the aboverelations may be modified for this purpose. For instance, it is usuallybeneficial for the extreme orders in neighboring tiles to be mutuallyadjacent in the spatial frequency space, rather than coinciding. Thissort of adjacency can be achieved using the technique described abovefor matching the grating periods and unit cell sizes of elements 48 and50, including the specific example of a 5 μm grating period of element50, 21×21 diffraction orders, and consequently a 52.5 μm unit cell sizefor element 48.

In practice, the ability to satisfy the relations exactly is mitigatedby the tolerances of DOE mastering, production and alignment. Therefore,for the purposes of the present patent application and the claims, apair of DOEs can be considered to satisfy the above relations if theirdiffraction characteristics match the angular criteria approximately, towithin a tolerance dictated by application requirements. For example, ina 3D mapping application, DOEs 48 and 59 may be considered to satisfythe above relations if tiles 56 overlap by no more than a certain numberof pixels, such as five pixels, in the images produced by image capturesubassembly 32.

In designing assembly 40, given one of the elements (such as element 48with a given tile divergence angle), the other element (such as element50) can be designed using the above relations and thus provide theappropriate fan-out for the given tile. When these relations aresatisfied, the tiling accuracy remains essentially unaffected by changesin the wavelength of light source 42 over the operating range ofelements 48 and 50, because the tile divergence angle and the fan-outangle will increase or decrease in concert.

DOEs 48 and 50 may be designed using methods known in the art fordesigning phase masks, such as the methods described above in theBackground section. Alternatively or additionally, rigorous designapproaches such as Rigorous Coupled Wave Analysis (RCWA), can be used,as described by Moharam and Gaylord in “Rigorous coupled-wave analysisof planar-grating diffraction” Journal of the Optical Society of America71:7, pages. 811-818 (1981), which is incorporated herein by reference.

The arrangement and design of optics 46 addresses the “zero-orderproblem” that is described in the above-mentioned US 2009/0185274: Aportion of input beam 44 (the zero diffraction order) may not bediffracted by the projection optics and may thus continue through to theprojection volume. In some DOE designs, the intensity of this zero-orderbeam may exceed eye-safety limits, particularly when laser illuminationis used, and may detract from the contrast of the pattern.

The design of elements 48 and 50 overcomes this potential problem.Specifically, by dividing the input beam into multiple output beams 52,element 50 inherently reduces the fraction of the input beam thatremains in the central output beam, typically to 1/9 (or less) of theinput beam energy in the 3×3 example shown in the figures. Furthermore,because the tile pattern generated by element 48 has a relatively smalldivergence angle (much smaller than the overall field of view), thephase mask of element 48 may be controlled precisely to suppress thezero-order component. Thus, in typical embodiments, the zero-ordercomponent of the diffraction pattern of optics 46 contains no more than1% of the energy of the input beam, and may contain substantially less.With appropriate design and manufacturing, the total zero ordercomponent from the combination of elements 48 and 50 can even be reducedbelow 0.1%.

It will be appreciated that the embodiments described above are cited byway of example, and that the present invention is not limited to whathas been particularly shown and described hereinabove. Rather, the scopeof the present invention includes both combinations and subcombinationsof the various features described hereinabove, as well as variations andmodifications thereof which would occur to persons skilled in the artupon reading the foregoing description and which are not disclosed inthe prior art.

The invention claimed is:
 1. Optical apparatus, comprising first andsecond diffractive optical elements (DOEs) arranged in series todiffract an input beam of radiation, wherein the first DOE is configuredto diffract the input beam so as to generate a pattern of spots in atile with a specified divergence angle, including spots corresponding toextreme diffraction orders of the first DOE at borders of the tile,while the second DOE is configured to split the input beam into a matrixof output beams with a specified fan-out angle, and wherein thedivergence and fan-out angles are chosen so as to project the radiationonto a region in space in multiple adjacent instances of the diffractionpattern, which tile the region, and wherein the extreme diffractionorders of neighboring tiles are mutually adjacent in a spatial frequencyspace.
 2. The apparatus according to claim 1, wherein the divergenceangle of each instance of the pattern is 2β_(Tile), and the fan-outangle between the adjacent instances is β_(FO), and wherein thedivergence and fan-out angles are chosen so that sin(β_(FO))=2sin(β_(Tile)).
 3. The apparatus according to claim 2, wherein adiffraction pattern of the apparatus includes a zero-order component,and wherein the first and second DOEs are configured to diffract theinput beam so that the zero-order component contains no more than 1% ofan energy of the input beam.
 4. The apparatus according to claim 1,wherein the first and second DOEs are configured so that the multipleadjacent instances of the pattern tile the region irrespective of awavelength of the input beam.
 5. The apparatus according to claim 1,wherein the second DOE is configured to distribute an energy of theinput beam among the output beams in accordance with a predefinednon-uniform distribution.
 6. The apparatus according to claim 1, whereinthe matrix of the output beams comprises at least a 3×3 matrix. 7.Mapping apparatus, comprising: a projection subassembly, comprising: aradiation source, which is configured to generate an input beam ofradiation; and first and second diffractive optical elements (DOEs)arranged in series to diffract the input beam, wherein the first DOE isconfigured to diffract the input beam so as to generate a pattern ofspots in a tile with a specified divergence angle, including spotscorresponding to extreme diffraction orders of the first DOE at bordersof the tile, while the second DOE is configured to split the input beaminto a matrix of output beams with a specified fan-out angle, so as toproject the radiation onto a region in space, wherein the divergence andfan-out angles are chosen so that the radiation is projected intomultiple adjacent tiles containing the pattern of spots, which tile theregion, such that the extreme diffraction orders of neighboring tilesare mutually adjacent in a spatial frequency space; an image capturesubassembly, which is configured to capture an image of the patternappearing on an object in the region; and a processor, which isconfigured to process the image so as to produce a three-dimensional(3D) map of the object.
 8. The apparatus according to claim 7, whereinthe divergence angle of each instance of the pattern is 2β_(Tile), andthe fan-out angle between the adjacent instances is β_(FO), and whereinthe divergence and fan-out angles are chosen so that sin(β_(FO))=2sin(β_(Tile)).
 9. The apparatus according to claim 7, wherein the firstand second DOEs are configured so that the multiple adjacent instancesof the pattern tile the region irrespective of a wavelength of the inputbeam.
 10. The apparatus according to claim 7, wherein the second DOE isconfigured to distribute an energy of the input beam among the outputbeams in accordance with a predefined non-uniform distribution.
 11. Theapparatus according to claim 7, wherein the matrix of the output beamscomprises at least a 3×3 matrix.
 12. The apparatus according to claim 7,wherein a diffraction pattern of the projection subassembly includes azero-order component, and wherein the first and second DOEs areconfigured to diffract the input beam so that the zero-order componentcontains no more than 5% of an energy of the input beam.
 13. A methodfor projection, comprising: directing an input beam of radiation to passin series through first and second diffractive optical elements (DOEs),wherein the first DOE is configured to diffract the input beam so as togenerate a pattern of spots in a tile with a specified divergence angle,including spots corresponding to extreme diffraction orders of the firstDOE at borders of the tile, while the second DOE is configured to splitthe input beam into a matrix of output beams with a specified fan-outangle, and wherein the divergence and fan-out angles are chosen so as toproject the radiation onto a region in space in multiple adjacent tilescontaining the pattern of spots, which tile the region, and such thatthe extreme diffraction orders of neighboring tiles are mutuallyadjacent in a spatial frequency space.
 14. The method according to claim13, wherein the divergence angle of each instance of the pattern is2β_(Tile), and the fan-out angle between the adjacent instances isβ_(FO), and wherein the divergence and fan-out angles are chosen so thatsin(β_(FO))=2 sin(β_(Tile)).
 15. The method according to claim 13,wherein directing the input beam comprises arranging the first andsecond DOEs so that the multiple adjacent instances of the pattern tilethe region irrespective of a wavelength of the input beam.
 16. Themethod according to claim 13, wherein the second DOE is configured todistribute an energy of the input beam among the output beams inaccordance with a predefined non-uniform distribution.
 17. The methodaccording to claim 13, wherein the matrix of the output beams comprisesat least a 3×3 matrix.
 18. The method according to claim 13, whereindirecting the input beam to pass through the first and second DOEscomprises generating a diffraction pattern that includes a zero-ordercomponent, and wherein the first and second DOEs are configured todiffract the input beam so that the zero-order component contains nomore than 5% of an energy of the input beam.
 19. The method according toclaim 13, and comprising capturing an image of the pattern appearing onan object in the region, and processing the image so as to produce athree-dimensional (3D) map of the object.